Phase Space Non-commutativity and its Stability

TL;DR

This paper explores how phase space non-commutativity influences system stability, demonstrating that quartic interactions satisfying copositivity can stabilize such systems, with detailed methods for perturbative analysis.

Contribution

It introduces a framework for analyzing stability in non-commutative phase space and shows how specific interactions can restore stability.

Findings

Non-commutativity can destabilize systems if strong enough.

Quartic interactions satisfying copositivity can stabilize non-commutative systems.

Provides detailed canonical and path integral methods for perturbative analysis.

Abstract

We consider a generalised non-commutative space-time in which non-commutativity is extended to all phase space variables. If strong enough, non-commutativity can affect stability of the system. We perform stability analysis on a couple of simple examples and show that a system can be stabilised by introducing quartic interactions provided they satisfy phase-space copositivity. In order to conduct perturbative analysis of these systems one can use either canonical methods or phase-space path integral methods which we present in some detail.